The Dynamics of Nonlinear Reaction-Diffusion Equations with Small Lévy Noise

Nonfiction, Science & Nature, Mathematics, Mathematical Analysis, Statistics
Cover of the book The Dynamics of Nonlinear Reaction-Diffusion Equations with Small Lévy Noise by Arnaud Debussche, Michael Högele, Peter Imkeller, Springer International Publishing
View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart
Author: Arnaud Debussche, Michael Högele, Peter Imkeller ISBN: 9783319008288
Publisher: Springer International Publishing Publication: October 1, 2013
Imprint: Springer Language: English
Author: Arnaud Debussche, Michael Högele, Peter Imkeller
ISBN: 9783319008288
Publisher: Springer International Publishing
Publication: October 1, 2013
Imprint: Springer
Language: English

This work considers a small random perturbation of alpha-stable jump type nonlinear reaction-diffusion equations with Dirichlet boundary conditions over an interval. It has two stable points whose domains of attraction meet in a separating manifold with several saddle points. Extending a method developed by Imkeller and Pavlyukevich it proves that in contrast to a Gaussian perturbation, the expected exit and transition times between the domains of attraction depend polynomially on the noise intensity in the small intensity limit. Moreover the solution exhibits metastable behavior: there is a polynomial time scale along which the solution dynamics correspond asymptotically to the dynamic behavior of a finite-state Markov chain switching between the stable states.

View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart

This work considers a small random perturbation of alpha-stable jump type nonlinear reaction-diffusion equations with Dirichlet boundary conditions over an interval. It has two stable points whose domains of attraction meet in a separating manifold with several saddle points. Extending a method developed by Imkeller and Pavlyukevich it proves that in contrast to a Gaussian perturbation, the expected exit and transition times between the domains of attraction depend polynomially on the noise intensity in the small intensity limit. Moreover the solution exhibits metastable behavior: there is a polynomial time scale along which the solution dynamics correspond asymptotically to the dynamic behavior of a finite-state Markov chain switching between the stable states.

More books from Springer International Publishing

Cover of the book The World Disorder by Arnaud Debussche, Michael Högele, Peter Imkeller
Cover of the book Empirical Philosophy of Science by Arnaud Debussche, Michael Högele, Peter Imkeller
Cover of the book Atlas of Elastosonography by Arnaud Debussche, Michael Högele, Peter Imkeller
Cover of the book Fundamentals and Advanced Techniques in Derivatives Hedging by Arnaud Debussche, Michael Högele, Peter Imkeller
Cover of the book Natural Disasters, Foreign Trade and Agriculture in Mexico by Arnaud Debussche, Michael Högele, Peter Imkeller
Cover of the book Urban Disaster Resilience and Security by Arnaud Debussche, Michael Högele, Peter Imkeller
Cover of the book Reasoning with Rough Sets by Arnaud Debussche, Michael Högele, Peter Imkeller
Cover of the book Nonlinear Elastic Waves in Materials by Arnaud Debussche, Michael Högele, Peter Imkeller
Cover of the book Sustainable Agriculture Reviews 33 by Arnaud Debussche, Michael Högele, Peter Imkeller
Cover of the book Entrepreneurship in Culture and Creative Industries by Arnaud Debussche, Michael Högele, Peter Imkeller
Cover of the book The Future Internet by Arnaud Debussche, Michael Högele, Peter Imkeller
Cover of the book Residual Stress, Thermomechanics & Infrared Imaging, Hybrid Techniques and Inverse Problems, Volume 9 by Arnaud Debussche, Michael Högele, Peter Imkeller
Cover of the book Transfer Pricing in SMEs by Arnaud Debussche, Michael Högele, Peter Imkeller
Cover of the book Earthquake Geotechnical Engineering Design by Arnaud Debussche, Michael Högele, Peter Imkeller
Cover of the book Contemporary Israeli–Turkish Relations in Comparative Perspective by Arnaud Debussche, Michael Högele, Peter Imkeller
We use our own "cookies" and third party cookies to improve services and to see statistical information. By using this website, you agree to our Privacy Policy